Re: Information re elements (ndot)

Bjoern Gimle@tt-tech.se (Gimle@tt-tech.se")
Thu, 29 Aug 1996 17:29:56 +0200

Vince Gardiner wrote :

>If this is in the too hard basket, (and I understand that you are busy
>people) would some-one explain what you mean when referring to ndot.
-- 
The AMSAT FAQ Tutorial calls this N1 ( and does not describe what they
probably call N2 in the next field ). I call it ndot2, to remember that
it is the derivative, divided by 2, of mean motion, which AMSAT call N0,
I call MM, and ought to call n.

Clear ??

The number of anomalistic orbits ( relative to perigee ) done T days
after the Epoch is approximately   T * ( N0 + T * ( N1 + T * N2 ) ).
Actually, the computation in the SGP model is much more complex,
since it adds periodic and secular disturbances from Earth's 
irregular gravity field, and computes the new position of the perigee
(AOP) and node (RAAN) needed for predicting the Earth-fixed position.

But if N1 (ndot, ndot2) is positive and not too small, we can estimate
the effect on N0, and the probable error in predicted time.

The new N0 would be   N0 + T * ( 2 * N1 + T * 3 * N2 ).

The effect of (mainly) atmospheric drag would be T * T * ( N1 + T * N2 )
orbits.

Often, the error in N1 is 20 % or more, and perhaps 50 % in N2,
so you could include the factors 0.2 and 0.5 into the formula
to estimate how early (or late) to expect the satellite; 
multiply by (approximately) 1440/N0 to get effect in minutes,
or by 360 to get degrees of MA (mean anomaly)
Example :
Molniya Rk                                       424 x 204
1 24274U 96045B   96234.10450674  .00239260  78472-5  30658-3 0   131
2 24274  62.8033 225.2582 0164710 131.8448 229.6812 15.85841280   986

A week later :
24274
1 24274U 96045B   96241.15729356 +.00407633 +79230-5 +48074-3 0 00382
2 24274 062.8041 198.0217 0145519 133.0010 228.3445 15.90583551002106